Initial sequences and Waldschmidt constants of planar point configurations

Abstract

The purpose of this work is to extend the classification of planar point configurations with low Waldschmidt constants initiated in [M. Dumnicki, T. Szemberg and H. Tutaj-Gasińska, Symbolic powers of planar point configurations II, J. Pure Appl. Algebra 220 (2016) 2001–2016] and continued in [M. Mosakhani and H. Haghighi, On the configurations of points in [Formula: see text] with the Waldschmidt constant equal to two, J. Pure Appl. Algebra 220 (2016) 3821–3825] for all values less than [Formula: see text]. As a consequence, we prove a conjecture of Dumnicki, Szemberg and Tutaj-Gasińska concerning initial sequences with low first differences.